Hi Francisco, yes, we do use it. You can write it "et cetera," (which is how it's pronounced), but it's much more common to write "etc."
"You name it" is used in a slightly different way. Usually you use "etc." at the end of a list to tell somebody that they can imagine the list continuing with similar things. For example, "When I go on a trip, I always pack shirts, pants, socks, shoes, etc."
Usually you use "you name it" to mean "anything and everything" or, "everything you can imagine." For example, "When he goes on a trip, he always packs swimsuits, snowsuits, skis, roller skates, beach balls, frisbees, you name it."